Geometry of Pellet Rolling Thread
In that thread I offered a proof of the geometry of pellet rolling showing what it differentiates upon. To wit: Head Radius, Skirt Radius, and distance between the two. Those are the only three things which the proof shows. Rolling does not give us meaningful information about pellet weight, thickness of skirt, or axial alignment. There are probably a host of other things which might be pointed at "roundness" for example.
The math here is intended to quantify the limits of the accuracy of the method when differentiating between the properties which it DOES differentiate upon.
Harry was kind enough to give us this information:
I have put that data into a spread sheet and calculated the following:
NOTE: Sorry I should have explained H1 is the distance from the index point to the center of the circle upon which the pellet rolled. R1 is the computed head diameter for that roll and R2 is the computed skirt diameter for that roll.
It says two thirds of the time a pellet will roll into the same point +/- one third of it's length and 100% of the time it will roll into a slot which is +/- two thirds of it's length. That is principally due to errors in the construction and use of the rolling machine itself and not the method. We can use that information when implementing our rolling table.
This implies that there is a trade off between effort and improvement when rolling pellets (who knew?
). Group sizes should decrease by about 1/3 with the first rolling. If you roll a second time it should again reduce by 1/3 of that and a third rolling would then reduce that by a third. So (1/3) + (2/9) + (3/27), if we convert that to percentages: 33.3+22.2+11.1=66.66% or two thirds. Another way to say that is this, "If you are shooting one MOA groups at some distance AND that group size is ENTIRELY due to the differences we are testing, after rolling your pellets three times your group statistically should be one third of an MOA." Do note that there are a LOT of conditionals in that sentence. Also note that fliers by definition will happen if you define a flier as any pellet that exceeds the standard deviation for the group. What we are doing with this method is reducing the standard deviation for the group by selecting upon three different criteria simultaneously.
Everyone knows what is said about statistics.
That's the math... now how do you build a more accurate machine? That's the next part.
In that thread I offered a proof of the geometry of pellet rolling showing what it differentiates upon. To wit: Head Radius, Skirt Radius, and distance between the two. Those are the only three things which the proof shows. Rolling does not give us meaningful information about pellet weight, thickness of skirt, or axial alignment. There are probably a host of other things which might be pointed at "roundness" for example.
The math here is intended to quantify the limits of the accuracy of the method when differentiating between the properties which it DOES differentiate upon.
Harry was kind enough to give us this information:
I have put that data into a spread sheet and calculated the following:
NOTE: Sorry I should have explained H1 is the distance from the index point to the center of the circle upon which the pellet rolled. R1 is the computed head diameter for that roll and R2 is the computed skirt diameter for that roll.
It says two thirds of the time a pellet will roll into the same point +/- one third of it's length and 100% of the time it will roll into a slot which is +/- two thirds of it's length. That is principally due to errors in the construction and use of the rolling machine itself and not the method. We can use that information when implementing our rolling table.
This implies that there is a trade off between effort and improvement when rolling pellets (who knew?
). Group sizes should decrease by about 1/3 with the first rolling. If you roll a second time it should again reduce by 1/3 of that and a third rolling would then reduce that by a third. So (1/3) + (2/9) + (3/27), if we convert that to percentages: 33.3+22.2+11.1=66.66% or two thirds. Another way to say that is this, "If you are shooting one MOA groups at some distance AND that group size is ENTIRELY due to the differences we are testing, after rolling your pellets three times your group statistically should be one third of an MOA." Do note that there are a LOT of conditionals in that sentence. Also note that fliers by definition will happen if you define a flier as any pellet that exceeds the standard deviation for the group. What we are doing with this method is reducing the standard deviation for the group by selecting upon three different criteria simultaneously.Everyone knows what is said about statistics.
That's the math... now how do you build a more accurate machine? That's the next part.
